The exchequer loses at least £5bn a year because the taxman is failing to crack down on "morally wrong" tax avoidance schemes similar to the one used by comedian Jimmy Carr, the chair of the Commons public accounts committee warns today.

Margaret Hodge, the former Labour minister, said rich businessmen designing the schemes were "running rings" around HMRC.

She said HMRC had an "appallingly bad record" at catching tax cheats, having fined just 11 people for promoting tax avoidance since 2004 – despite 10,000 people a year coming forward to report tax avoidance schemes.

A report by the PAC published on Tuesday says there is "a lot of money to be made in selling avoidance schemes", and commissions paid to the creators of the schemes can be up to 20% of the tax saved.

Hodge told Lin Homer, chief executive and permanent secretary of HMRC, that she didn't want to be "aggressive and awful about it", but the agency's failure to crack down on tax avoidance was "gobsmacking".

"There has been huge growth, and appalling proliferation [in tax avoidance], and what has HMRC been up to? It has only taken 11 cases to tax tribunals," she said.

The 11 tax avoidance promoters taken to tribunal were fined just £5,000 each despite the maximum penalty being £1m. Hodge said HMRC had never fined an individual for failing to disclose a scheme on their tax return.

Hodge said HMRC must "robustly" crack down on tax avoidance promoters that are "costing the country billions, as the public are struggling with less money in their pockets". She added: "It offends the sense of fairness."

She called on tax avoiders and the businesses creating tax avoidance schemes to be "named and shamed".

Hodge said businessmen promoting schemes such as those used by Jimmy Carr, Gary Barlow and Wayne Rooney were winning a "game of cat and mouse" with HMRC, responding to the discovery of their schemes by moving on to create new ones.

At the public accounts committee (PAC) hearing Aiden James, director of Tax Trade Advisers, a specialist in income tax avoidance, told MPs that all of the schemes his company previously marketed were now illegal.

Ian Swales, a Liberal Democrat member of the PAC, asked: "All the schemes you have marketed are now illegal, so you are now looking for the next loophole – is that a fair description of your business?" To which James replied: "That is how it works, yes."

Hodge said HMRC only knows about 46% of tax avoidance schemes, and that if HMRC does track down a scheme that breaks the rules the promoter calls in barristers to plead that it had a "reasonable excuse" for not disclosing the scheme in order to escape a fine.

At the hearing she named QCs Jonathan Peacock, Rex Bretten, Andrew Thornhill and Giles Goodfellow as "the guys who prostitute themselves to these schemes".

On top of the £5bn a year known to be lost to tax schemes, Hodge said HMRC had very little hope of collecting a further £10.2bn. "We are desperate to grow the economy. Just think of the houses we could build and the pot holes we could fill with [these lost taxes] without adding to our [national] deficit," she said. "It's megabucks."

The PAC named Future Capital Partners and Ingenious Media as companies exploiting government tax breaks intended to encourage the film industry to help the rich avoid tax.

Famous participants in schemes organised by Ingenious include footballers Steven Gerrard and Wayne Rooney and pop stars Peter Gabriel and Robbie Williams. Films financed by Ingenious include Avatar, Die Hard 4 and Die Hard 5 and Girl with the Pearl Earring.

Typically, film partnership schemes are structured to allow investors to delay tax payments on investments over long periods of time. In many cases the financial gain from this delay can exceed the end tax liability.

Patrick McKenna, chief executive of Ingenious, has said he is "at a loss to understand why it may be considered that we market tax avoidance schemes".

Hodge told him: "You were exploiting a well-intentioned tax relief to try to get individuals, and god knows who else, to mitigate their taxes."

The Treasury has said it will provide HMRC with £77m of extra funds a year for two years to help it track down wealthy individuals and companies that tried to avoid paying tax. A spokesman for HMRC said: "We are glad the report exposes the practices of promoters who sell tax avoidance schemes to wealthy individuals. In the last year alone the courts have ruled in HMRC's favour in multiple tax avoidance cases where over £1bn has been protected.

"Additionally the government recently announced an extra £77m in HMRC funding to tackle evasion and aggressive avoidance; we have also consulted on strengthening the regulations around these schemes; and, for the first time ever, this government is introducing a general anti-abuse rule which will make it even harder for people to avoid paying their share of tax."